AP Free - Response Question HELP iNCLUDES angular velocity and acceleration

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The discussion focuses on solving a physics problem related to angular velocity and acceleration from an AP Free Response question. The user is struggling with calculating the tension in a string and has attempted to apply equations involving mass, angular velocity, and moment of inertia but feels their answers are incorrect. They express confusion about the relationship between angular and linear velocity and seek clarification on these concepts. Additionally, there is a question about current usage in a resistor, indicating a broader inquiry into electrical concepts. The user is looking for guidance to correctly approach and solve the mechanics problem.
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AP Free - Response Question HELP! iNCLUDES angular velocity and acceleration

http://www.fayar.net/east/Teacher.web/Math/young/APPC/APPC%201999/physics_c_m_99.pdf

Mechanics 3 is the problem I really need help on.
I tried to find the tension of the string by setting it equal to mg + Iwr, but I'm not sure if I'm doing it right! On part b, I set the angular acceleration equal to the initial angular velocity + moment of inertia, and I got through canceling some factors. On part c, I set the angular velocity equal to the linear velocity times the time.

I NEED HELP ON HOW TO DO IT RIGHT! I THINK I'M TOTALLY DOING IT WRONG BECAUSE MY ANSWERS SEEM TO BE WAY OFF!
 
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Its a string, so it can only support load in the axial direction.
 
Is current used up in a resistor? Explain
 

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